The subject of this thesis is the problem of computing the visibility graph of m points P within a polygon Q. The vertices of the visibility graph are the points of P and the edges of the graph are the pairs of points in P×P , where the line between them is fully contained inside Q. Known algorithms by Ben-Moshe et al. are presented for computing the visibility graph of a simple polygon, the vi...

The visibility graph V(P ) of a point set P ⊆ R has vertex set P , such that two points v, w ∈ P are adjacent whenever there is no other point in P on the line segment between v and w. We study the chromatic number of V(P ). We characterise the 2and 3-chromatic visibility graphs. It is an open problem whether the chromatic number of a visibility graph is bounded by its clique number. Our main r...

A shape visibility representation displays a graph so that each vertex is represented by an orthogonal polygon of a particular shape and for each edge there is a horizontal or vertical line of sight between the polygons assigned to its endvertices. Special shapes are rectangles, L, T, E and H-shapes, and caterpillars. A flat rectangle is a horizontal bar of height > 0. A graph is 1-planar if th...

The problem of aggregation is considerable importance in many disciplines. In this paper, a new type of operator called visibility graph averaging (VGA) aggregation operator is proposed. This proposed operator is based on the visibility graph which can convert a time series into a graph. The weights are obtained according to the importance of the data in the visibility graph. Finally, the VGA o...

In this paper we give graph-semantics to a fundamental part of the semantics of the service modeling language SRML. To achieve this goal we develop a new graph transformation system for what we call 2-level symbolic graphs. These kind of graphs extend symbolic graphs with a simple 2-level hierarchy that can be generalized to arbitrary hierarchies. We formalize the semantics using this new graph...

A graph is called a strong ( resp. weak) bar 1-visibility graph if its vertices can be represented as horizontal segments (bars) in the plane so that its edges are all (resp. a subset of) the pairs of vertices whose bars have a -thick vertical line connecting them that intersects at most one other bar. We explore the relation among weak (resp. strong) bar 1-visibility graphs and other nearly pl...

objective midazolam is a significant and effective drug for control of a life-threatening condition, generalized and partial refractory convulsive status epilepticus. the goal of this study was evaluation of midazolam efficacy for management of this serious disease and its two side effects, hypotension and respiratory failure. materials & methods our study was done using a quasi experimental me...